Question

Explain briefly how the de Broglie relation Where's experimentally verified in case of electrons

Answer 1

De Broglie derived his equation using well established theories through the following series of substitutions:

1. De Broglie first used Einstein’s famous equation relating matter and energy:
$E=m{c}^2$ (0)
With
a) E = energy
b) M = mass,
c) C = speed of light

2. Using Planck's theory which states every quantum of a wave has a discrete amount of energy given by planck’s equation:
E=hv (1)
With
a) E= energy,
b) H= Plank’s constant $(6.62607\times {10}^{-34}Js)$,
c) V= frequency

3. Since de Broglie believed particles and wave have the same traits, he hypothesized that the two energies would be equal.
$m{c}^2=hv$ (2)
4. Because real particles do not travel at the speed of light, De Broglie submitted velocity (v) for the speed of light (c).
$m{c}^2=hv$ (3)
5. Through the equation .$\lambda$ De Broglie substituted $\frac{v}{\lambda }$ for v and arrived at the final expression that relates wavelength and particle with speed.
$m{v}^2=\frac{hv}{v}$ (4)
Hence:
$\lambda =\frac{hv}{m{v}^2}=\frac{h}{mv}$ (5)
A majority of wave-particle duality problems are simple plug and chug via 5 with some variation of cancelling out units.